The reservoir, or expansion tank as it's sometimes called, is a semi-transparent plastic bottle that may be pressurized or non-pressurized. The reservoir usually has level markings for quick checking of the coolant level.
The reservoir allows for expansion of the coolant when the engine is warm, rather than having the coolant spill out of an overflow tube. When connected to the radiator with a properly functioning pressure cap, the reservoir enables the radiator to be consistently full, regardless of temperature.
Check the coolant level at least every oil change; weekly is even better. A reservoir that consistently drops in coolant level after topping off usually indicates a leak. The hose between the reservoir and radiator may be loose or damaged, the pressure cap may be faulty, or there may be a leak elsewhere in the cooling system. If your inspection of the system provides no clues, have the cooling system pressure tested and checked by a qualified professional.